Week10

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Bartolini Bussi & Mariotti (2008)
  • I am having difficulties in getting a clear picture of what the differences and roles of Artifact signs, Pivot sings and Mathematical sings are; does anyone have a clever way of thinking about it? (JMG) (DOS)
  • It seems that on p748 an artifact is an item, and an artifact coupled with a utilization scheme is an instrument, which seems analogous to the signified/signifier/sign structure, but then on p753 the idea of signs are introduced. Is there a difference between instruments and signs when looking across papers (ie Presmeg's use of signs) or within the current paper, or is there a distinction between instruments and signs that I am missing? (JMG)
  • On page 778, the authors point to a key distinction between Vygotskian and socio-constructivist (referencing Cobb's work) perspectives, with regards to the symmetry or asymmetry of the roles of teacher and students. How can we elaborate upon this distinction, while remaining true to the readings thus far in the semester? How does their use of the term didactic throughout the paper connect to this distinction? (JLK)
  • The authors use excerpts to illustrate the examples of different abaci and the use of Cabri. How do the differences in these two excerpts help to paint the picture of (the authors' view of) semiotic mediation? (JLK)
  • How does the role of the author's system of signs relate to their theoretical framework regarding semiotic mediation as supported by the abacus and cabri examples? (AJ) (DOS)
  • In what ways are the teacher moves (and their interpretation of those moves) shown in these examples consistent with the authors' theoretical framework? What would conducting research from this perspective look like? (DOS)
  • On page 777, the author's chose the abacus and cabri artifacts based on its "semiotic potential." What makes different artifacts more potential than others and how does that fit with their theoretical framework? (AJ)





Presmeg (2006)
  • Presmeg makes multiple statements connecting her discussion of semiotics to Sfard's use of the term reification. How might Presmeg's use of the term differ from Sfard's use of it? (JLK)
  • At the bottom of page 172, Presmeg states that "[e]ach interpretant involves the negotiation of meaning through discourse". Do Vygotsky's conceptions about thinking apply here? Why or why not? (JLK)
  • Bartolini Bussi & Mariotti make use of a semiotic chain from artifact signs to the mathematical signs (with use of the pivotal signs). Presmeg's notion of nested chaining model offers a web of signs that indicate changes in discourse (e.g., see diagram on p. 166). How does the nature of discourse change during this process (given perhaps the 'falling back' notion or Sfard's reification process)? (AJ)


  • (not-so-important) What ARE the implications for the "Connections Standard", according to Presmeg? Do we need to go back to the abstract to finish the discussion section? Is this typical for scholarly writing? (JLK)


van Oers (2000)
  • What does the discussion of the "semiotically more capable person" on pages 139 (definition of ZPD) and 161 imply in terms of what Bartolini et. al refer to as symmetric and asymmetric teacher-student roles (JLK)
  • The authors use the example of the "shoe store" to demonstrate non-mathematical (at least, not directly mathematical) treatment of semiotics. Why are the authors committed to the notion that students should develop facility with sign creation and refinement in a variety of contexts? What "Connections" might this stance have, with regards to Presmeg's article? (JLK)
  • Semiotic activity arose out a situation of play will some actions by the teacher to move things along. I can see how this is effective and how starting early on in childhood with this focus is helpful. My question is what would a curriculum look like that could accomplish this? What are the implications for curriculum design? (DOS)
  • On page 169 the author states that one of the shortcomings of modern constructivist analyses of math ed is that construction as a cognitive process is conceived as a nondevelopmental mechanism. To what extent do we agree, disagree, or find irrelevant, this statement (given what we have read about constructivism, noting that we not have an overview of modern constructivist analysis) (DOS)

  • Across all readings: In what ways are the authors' views of semiotics different? (DOS)


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Outline For Class Discussion
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Focus Question: In what ways are the authors' views of semiotics different?
Conceptualization of semiotic mediation (in general, formative terms)

Bussi & Mariotti
  1. Review/summarize the authors' framework (and artifact, pivot, and mathematical signs)
  2. Comments on the example of the abaci in terms of semiotic mediation
  3. Comments on the example of Cabri in terms of semiotic mediation
  4. Relating abaci and Cabri examples back to the framework (differences)


Presmeg
  1. The term Connections, as used by the author (to help review the article - i.e. how does the term align with the author's discussion of semiotics)
  2. What is semiotic chaining?
  3. What are the implications from figure 3 (page 169)?
  4. Review and discussion Sfard's reification, and connect it to Presmeg's nested chaining model (p 166&170)

van Oers
  1. Review of semiotic activity arising out of play and the implications of it
  2. What does the discussion of the "semiotically more capable person" imply?




Across the readings:
  1. In what ways are the authors' views of semiotics different and/or similar?




Introduction to Dorfler

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Notes From Class Discussion
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Bussi & Mariotti
  • p 752 Definition of mediation. "Fostering a relation between", a mediator mediating on the mediated. Need to include the notion of semiotics
  • Semiotic mediation: The model that represents the framework is found on page 757 (figure 28.2). Artifact signs, pivot signs, and mathematical signs, task, artifact, mathematics culture
  • p. 748. Distinction between artifacts and instruments. Artifact is just some object, whereas instruments also come with knowledge on how to use it (utilization schemes). Analogy to a hammer. A hammer by itself is just an artifact. Using it to drive a nail into a board is the use of it as an instrument. Later using it to hit Dustin is the use of it as an instrument with a different purpose (thus, it is a different instrument).
  • Artifact signs (p. 756). CONTEXT of the use of the artifact (what;s the purpose/context for the use of the hammer?)
  • Mathematics signs (specific to the mathematics context)
  • Pivot signs. Refer to both mathematical and artifact signs. Is this like a chaining process? (see example on page 757). Process of generalization of getting to the definition of function.
  • Function as an example to illustrate the three types.
  • Examples of linear, exponential, etc. etc. (function families, parent functions)
  • How is the term tools used here (maybe read Rabardel to clarify)
  • Assumption of the use of artifacts (operations carried out with artifacts)
  • Abaci example (focus is placed more on the transition from artifact to mathematical signs, rather than on a clear exposition on the pivot signs). Ambiguous use of pivot signs
  • Slavonic abacus ()
  • The use of Cabri (dragging and trace tools as artifact signs)

Presmeg
  • How is her semiotic chaining different from Gravemeijer's? Gravemeijer's seemed to impy a linear sequence of signifier, signified, signifier, signified, etc. etc.
  • Inclusion of nested signs.
  • Reference to the "falling back" (Pirie & Kieren, 1994)
  • The meaning maker (inclusion of the "I"). The interpretant. Not just between signifier and signified. We have an individual and a collective process of negotiation of meaning.
  • The treatment of meaning is similar to the use in Bussi & Mariotti's (except for diadic vs triadic models)
  • "R" is the signifier, "O" is the signified (page 171)
  • The meaning arrow is used to show the collection, unification, reification, encapsulation, attaching signifier to signified.
  • signifier comes before signified.
  • The interpretant indicates the reification/encapsulation (at the local level).
  • The interpretant is the result of the meaning maker acting on the signifier and signified (or the "O" and the "R").
  • The distinction between metaphor and metonymy


van Oers
  • Abbreviation. parallel (in epistemelogical sense) to Sfard's reification. In the bird example, "the extended identification process has been abbreviated into an 'immediate' recognition" (p. 144)
  • Predication is the developing of meaning
  • "predicate" = signified